Why does J/molC equal J/molK?

Because the measure is of change in energy per amount per change in temperature.

Kelvin and Celcius use the same scale for change in temperature, just with a different zero position.

Well, J/molC equals J/molK because the letters "C" and "K" got together one day and decided to have a party. They figured, "Hey, why not dress up as units of energy and confuse everyone?" So, they put on their fancy "J/mol" costumes and danced the night away, leaving scientists scratching their heads ever since. But hey, at least they're equal, so we don't have to worry too much about it!

The equality between joules per mole of carbon (J/molC) and joules per mole Kelvin (J/molK) is based on the fact that both units represent the same physical quantity, which is molar heat capacity. The molar heat capacity of a substance is defined as the amount of energy required to raise the temperature of one mole of the substance by one Kelvin (or one degree Celsius).

When we express molar heat capacity in J/molC, it indicates that the temperature change is measured in degrees Celsius. On the other hand, when we express molar heat capacity in J/molK, it means that the temperature change is measured in Kelvins. Since one Kelvin is equal to one degree Celsius, the numerical value of molar heat capacity remains the same regardless of whether it is expressed in J/molC or J/molK.

The equality between J/molC (Joules per mole degree Celsius) and J/molK (Joules per mole Kelvin) arises due to the nature of the temperature scales we use. The Kelvin (K) scale is an absolute temperature scale that measures temperature from absolute zero, where all molecular motion theoretically ceases. In contrast, the Celsius (C) scale is a relative temperature scale that is based on the freezing and boiling points of water.

To understand why J/molC equals J/molK, we need to recognize that one degree Celsius is equivalent to one Kelvin. In other words, the size of one degree Celsius is the same as one Kelvin. This means that the temperature intervals on both scales are the same, making the conversion between them straightforward.

Therefore:

1 J/molC = 1 J/molK

If you need to convert from one unit to the other, you simply need to multiply or divide by a factor of 1, which does not change the value.